V Quantum Physics (Chapter 33-35) quantum physics量子物理学
量子力学第二版(周世勋)
2µ
2µ
= qBnη = nB ⋅ qη
2µ
2µ
= nBNB ,
其中， M B
=
qη 2µ
是玻尔磁子，这样，发现量子化的能量也是等间隔的，而且
具体到本题，有
∆E = BM B
根据动能与温度的关系式
∆E = 10 × 9 × 10−24 J = 9 × 10−23 J
E = 3 kT 2
以及
1k ⋅ K = 10−3 eV = 1.6 × 10−22 J
∂ ∂r
(1 eikr ) − r
1 eikr r
∂ ∂r
(1 r
e
−ikr
ρ )]r0
=
iη [1 (− 2m r
1 r2
+ ik 1) − 1 (− rr
1 r2
−
ik
1 r
)]ρr0
可见，
ρ J2
=
−
ηk mr 2
ρr0
=
−
ηk mr 3
ρr
与rρ反向。表示向内(即向原点) 传播的球面波。
补充：设ψ (x) = eikx ，粒子的位置几率分布如何？这个波函数能否归一化？
1．3 氦原子的动能是 E = 3 kT （k 为玻耳兹曼常数），求 T=1K 时，氦原子的德布罗意波 2
长。
解 根据
2
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知本题的氦原子的动能为
1k ⋅ K = 10−3 eV ，
E = 3 kT = 3 k ⋅ K = 1.5 ×10−3 eV , 22
解 关于两个光子转化为正负电子对的动力学过程，如两个光子以怎样的概率转化为正 负电子对的问题，严格来说，需要用到相对性量子场论的知识去计算，修正当涉及到这个过 程的运动学方面，如能量守恒，动量守恒等，我们不需要用那么高深的知识去计算，具休到 本题，两个光子能量相等，因此当对心碰撞时，转化为正风电子对反需的能量最小，因而所 对应的波长也就最长，而且，有
朗道十卷英文名
朗道十卷英文名朗道十卷是世界著名物理学教材。
朗道十卷英文名如下所示。
一、《朗道理论物理学教程第一卷：力学》Course of Theoretical Physics Volume one: Mechanics二、《朗道理论物理学教程第二卷：场论》Course of Theoretical Physics Volume two: The Theory of Fields三、《朗道理论物理学教程第三卷：量子力学(非相对论理论) 》Course of Theoretical Physics Volume three: Quantum Mechanics (Non-relativistic Theory)四、《朗道理论物理学教程第四卷：量子电动力学》Course of Theoretical Physics Volume four: Quantum Electrodynamics 五、《朗道理论物理学教程第五卷：统计物理学》Course of Theoretical Physics Volume five: Statistical Physics六、《朗道理论物理学教程第六卷：流体动力学》Course of Theoretical Physics Volume six: Fluid Mechanics七、《朗道理论物理学教程第七卷：弹性理论》Course of Theoretical Physics Volume seven: Theory of Elasticity八、《朗道理论物理学教程第八卷：连续介质电动力学》Course of Theoretical Physics Volume eight: Electrodynamics of Continuous Media九、《朗道理论物理学教程第九卷：统计物理学》Course of Theoretical Physics Volume nine: Statistical Physics十、《朗道理论物理学教程第十卷：物理动理学》Course of Theoretical Physics Volume ten: Physical Kinetics。
半导体物理学(第7版)第四章习题及答案
第四章习题及答案1. 300K 时，Ge 的本征电阻率为47Ωcm ，如电子和空穴迁移率分别为3900cm 2/( V.S)和1900cm 2/( V.S)。
试求Ge 的载流子浓度。
解：在本征情况下，i n p n ==,由)(/p n i p n u u q n pqu nqu +=+==111σρ知 3131910292190039001060214711--⨯=+⨯⨯⨯=+=cm u u q n p n i .)(.)(ρ 2. 试计算本征Si 在室温时的电导率，设电子和空穴迁移率分别为1350cm 2/( V.S)和500cm 2/( V.S)。
当掺入百万分之一的As 后，设杂质全部电离，试计算其电导率。
比本征Si 的电导率增大了多少倍？ 解：300K 时，)/(),/(S V cm u S V cm u p n ⋅=⋅=225001350，查表3-2或图3-7可知，室温下Si 的本征载流子浓度约为3101001-⨯=cm n i .。
本征情况下，cm S +.u u q n pqu nqu -p n i p n /.)()(6191010035001350106021101-⨯=⨯⨯⨯⨯=+=+=σ金钢石结构一个原胞内的等效原子个数为84216818=+⨯+⨯个，查看附录B 知Si 的晶格常数为0.543102nm ，则其原子密度为322371051054310208--⨯=⨯cm ).(。
掺入百万分之一的As,杂质的浓度为3162210510000001105-⨯=⨯⨯=cm N D ，杂质全部电离后，i D n N >>，这种情况下，查图4-14（a ）可知其多子的迁移率为800 cm 2/( V.S)cm S .qu N -n D /.''468001060211051916=⨯⨯⨯⨯=≈σ比本征情况下增大了66101210346⨯=⨯=-..'σσ倍 3. 电阻率为10Ω.m 的p 型Si 样品，试计算室温时多数载流子和少数载流子浓度。
医学英语词汇（Q-R）_医学英语词汇
q. (electric quantity) 电量q-factor q因数（抗阻比因数，谐振线路或线圈的定格，z/r，或简称q）qt (quart) 夸脱（1/4加仑）quadrangle ①四角形②四角器quadrangular arm-sling 四角臂吊带quadrangular mitella 四角臂吊带puadrant ①象限仪②象限quadrate 正方形quadri- 四，四倍quadrivalent element 四价元素quadrupole residual gas analyser 四极残余气体分析仪qualification ①合格②规格qualification test 合格试验，鉴定试验qualimeter x射线透度计，x射线硬度计（测x射线之硬度）qualitative analysis 定性分析quality ①性质，质量②规格quality certificate 品质证明书quality claim 品质索赔quality inspection 品质检验quality specification 质量说明书quantifier 计量器quantimet 定量电视显微镜quantimeter x射线放射量计（测量由球管产生的x射线量）quantitative 定量的，数量的quantitative autoradiography 定量放射自显影术，定量自体放射照像术quantitative cytophotomety 定量细胞光度学quantitative determination 定量测定quantitative filter paper 定量滤纸quantitative fluorometer 定量荧光计quantitative microscope 定量显微镜quantitive 定量的，数量的quantity 数量，参量quantity claim 数量索赔quantity of electricity 电量quantity of heat 热量quantivalence 化合价，原子价quantizer ①数字转换器②量化器③编码器quantometer ①光量计②光谱分析计③辐射强度测量器quantorecorder ①光量计②辐射强度测定计1uantum ①量子②定量quantum biology 量子生物学quantum constant 量子常数quantum mechanics 量子力学quantum number 量子数quanrantine ①检疫期②检疫所quanrt (abbr. qt.) 夸脱（四分之一加仑）quarter ①季度②一刻钟③四分之一quartz 石英，水晶（即二氧化硅）quartz crystal 石英晶体1uartz filter 石英滤波器quartz glass 石英玻璃quartz lamp 石英灯quartz oscillator 石英振荡器quartz prism 石英棱镜quartz thermometer 石英温度计quartz transducer 石英换能器，石英传感器quasi- 半，似，拟，准quasiconductor 半导体quasi-insulator 准绝缘体quasi-monochromatic 准单色的quasi-static 似稳的，准静态的quench circuit 猝灭电路quenchometer 冷却速度试验器quernstone 磨石query 询问，质问quest 探索，寻找question 问题，探究quick 快的，迅速的quick access memory 快速存取存储器quick freeze chamber 快速冷冻室quicklime 生石灰，氧化钙quick-loading cassette 快速换片暗盒quick-silver 汞，水银quinhydrone electrode （醌）氢醌电极quotation 估价单，报价单quotation date 报价日期quote 开价，报价，开估价单qutient 商数，系数q wave q波（心电图）r (①reaumur temperature scale ②registered trademark ③ro-entgen) ①列氏温度计②注册商标③伦琴（x线量单位）ra (radium) 镭rabbet ①插孔，塞孔②槽，凹部rabbet cage 兔笼rabbit-ear antenna （电视）兔耳形天线（室内用）r-acg (right-apexcardiongram) 右心尖搏动图rachi- 脊柱rachial 脊柱的rachialbuminimeter 脑脊液白蛋白定量器，脊髓液蛋白计rachigraph 脊柱描记器rachio- 脊柱rachiometer 脊柱弯度计rachiotome 脊椎刀，椎骨刀rachitome 脊椎刀，椎骨刀rack 支架，格栅rack mounting 支架安装rad 拉德（辐射吸收剂量单位）radar 雷达radar therapy apparatus 射频治疗机radi (radiographic inspection) x射线检查radiability x射线透过性radiable x射线可透的radiac 放射性检测仪器，剂量探测仪radiacmeter ①剂量计②核辐射测定器radiagraph 活动焰切机radial grating 射线光栅radian 弧度radiant 放射的，辐射的radiant energy 辐射能radiant flux 辐射通量radiant heat lamp 辐射热灯radiant matter 辐射质radiant warmer 辐射加温器radiate ①辐射状②辐射，发光radiathermy 短波透热法radiation ①辐射，放射②放射疗法radiation counter 放射线计算器radiation distribution computer 放射线分布指示计算机radiation dose 辐身射剂量radiation equipment 放射线设备radiation heating apparatus 辐射热仪radiation monitor 放射检测器radiation protecting equipment x射线防护设备radiation survey meter 辐射测试仪radiation therapy 放射疗法，辐射疗法radiation trap 辐射捕集器，辐射护墙radiator ①放射器，辐射器②散热器radical ①根，基②基本的radio ①无线电设备②射电的，射频的radio- ①放射，辐射②无线电radioactive 放射性的radioactive carbon 放射性碳radioactive cobalt 放射性钴radioactive constant 放射性常数radioactive contaminant 放射性污染物radioactive decay 放射性衰变radioactive disintegration 放射性元素蜕变radioactive element 放射性元素radioactive emanation 放射性射气radioactive indicator 放射性示踪剂radioactive isotope 放射性同位素radioactive isotope renography 放射性同位素肾造影术radioactive marker 放射性标记物radioactive sample 放射性样品radioactive source 放射源radioactive tracer 放射性同位素示踪剂radioactivity 放射性，辐射性radioactor 镭疗器radioautogram ①自动射线摄影②放射性同位素示踪图③无线电传真radioautograph 放射自显影术radioautography 放射自显影术radiobroadcasting 无线电广播，用无线电传送radiocalcium 放射性钙，射钙radiocarbon 放射性炭，射炭radiocardiogram 放射心电图radiocardiography 放射心电描记法radiochemistry 放射化学radiochlorine 放射性氯，射氯radiochromatogram camera 放射色谱图摄影机radiochrometer ①x射线透度计②放射色谱计radiocinematograph x射线电影装置，x射线活动摄影机radiocinematography x射线活动照像术radiocirculography 放射血循环描记术radiocobalt 放射性钴，射钴radiode 镭插入器，镭锭仪（装镭锭用于治疗的仪器）radiodiagnosis 放射诊断，x射线诊断radiodiaphane 镭透照镜（进行镭透照检查的仪器）radio ecg transmission 无线电遥控心电图传送radioelectrocardiogram(abbr. recg) 放射心电图radioelectrocardiograph (abbr. recg) 放射心电图机radioelectrocardiography 放射心电图描记法radioelectroencephalogram（abbr. reeg）放射脑电图radioelectroencephalograph (abbr. reeg) 放射脑电图描记器radioelectromyogram (abbr. remg) 放射肌电图radioelectromyograph (abbr. remg) 放射肌电图描记器radioelectrophysiologram 放射电生理描记图radioelectrophysiolograph 放射电生理描记器radioelectrophysiolography 放射电生理描记术radio element 放射性元素radioencephalogram (abbr. reg) 放射脑电图radioencephalograph 放射脑电图机radioencephalography 放射脑电图描记法fadio-frequency 射频，无线电频率radio-frequency accelerator 高频加速器radio-frequency pacemaker 射频起搏器（心）radiogen 放射物质radiogram x射线照片radiograph x射线照片radiographer 放射照像技术员radiographic 放射照像的radiographic contrast x射线照像对比radiographic equipment x射线照像装置radiographic negative x射线底片radiographic sensitivity 抗射线感光度radiographic stereometry 立体x射线片测定法radiograph microfilm reducer 35毫米显微胶片摄影缩微器radiography x射线照像术radiography cone x射线摄影孔radiography of fistula 瘘管造影术radiography of lacrimal duct 泪道造影术radiography of parotids 腮腺造影术radiography unit x射线机radio-immunity 放射免疫radioimmunoassay (abbr. ria) 放射免疫测定（法）radioimmunoassay centrifuge 放射免疫测定离心机radioimmunoassay system 放射免疫分析仪radioimmunoelectrophoresis 放射免疫电泳（法）radioiodine 放射性碘，射碘（常用131i）radioisotope (abbr. ri) 放射性同位素radioisotope diagnostic unit 放射性同位素诊断仪radioisotope dynamic functiontesting unit 放射性同位素动态功能测定仪radioisotope generator 放射性同位素发生器radioisotope renogram apparatus 肾放射图仪radioisotope renogram examination apparatus 放射性同位素肾图仪radioisotope renograph 放射性同位素肾图检查仪radioisotope renography 放射性同位素肾图检查radioisotope scanning （放射性）同位素扫描radioisotope teletherapy unit 放射性同位素深部治疗机radioknife 高频手术刀（10mhz以上）kradiokymography x射线动态摄影术，x射线记波照像术radiolead 放射性铅，射铅radiolocator 无线电定位器radiologic(al) 放射性的，放射学的radiological apparatus x射线机radiologist 放射科医师radiology 放射学radiolucency 射线透射性，x射线可透性radiolus 探子radiometer ①辐射仪②放射量测定仪radiometry 放射性测量radiomicrometer 测微辐射计，辐射微量计radiomovies 电视电影，电视影片radionuclide 放射性核素radionuclide brain imager 放射性核素脑部摄像机radionuclide image intensifier 放射性核素影像增强器radionuclide imaging 放射性核素造影术radiopadcity x射线不透性radioparency x射线可透性，射线可透性radioparent x射线可透的，射线可透的radioparent sternal blade x射线可透胸骨刀radiophosphorus 放射性磷，射磷radiophotography x射线照像术radiophotoscanning 放射照像扫描术radioprotector 辐射防护装置radioplmonography 放射肺换气率测定法radiosclerometer x射线透度计，x射线硬度计radioscope ①x射线透视屏②放射探测仪③放射镜radioscopy 放射检查，x射线透视检查，荧光屏检查radio set ①收音机②无线电台radiostereoscope x射线实体透视镜radiostereoscopy x 射线实体透视检查，x射线脏器检查法radiosterilization 辐射消毒，放射性消毒radiosurgery 放射外科学，镭外科学（以镭锭进行外科治疗）radiotelemetry 无线电遥测术radiotelescope 电望远镜，无线电望远镜radiotelevisor 电视接收机radiotherapeutics 放射疗法radiotherapy 放射疗法radiotherapy equipment 放射治疗设备radiotherapy linear accelerator 放疗用直线加速器radiotherapy simulator 放射治疗模拟定位机radiothyroxine 放射性甲状腺素radiotomy 断层x射线照像术，体层x射线照像术radiotracer 放射性示踪元素radiotransmitter 无线电发报机radiotransparent x射线可透的，透x射线的radiovision 电视radio wave 无线电波radium (abbr. ra) 镭radium applicator 施镭器radium cannon 镭管cadium container 镭容器radium emanation 镭射气radium needle 镭针nadiumotherapy 镭疗法radium-plaque adaptometer 镭板适应计radium recovery service 镭换置设施radium tube 镭管radius ①桡骨②半径radiuscope 眼晶状体半径测量仪radius splint 桡骨夹板radon (abbr. rn) 氡，镭射气radon container 氡容器rafting 合金，熔合物rail 轨道，导轨railway 铁路，轨道railway catheter 槽式导管rain 雨raincoat 雨衣raise 提高，增加，举起ram (radioactivity monitoring) 放射性监测ramp ①接线夹②斜面，滑行台rancidify 酸败random 无规则的，任意的，随机的random access memory 随机存取存储器（计算机）randomization 随机取样，随机化（统计学）randomness 随机性random number 随机数random sampling 随机抽样random zero sphygmomanometer 随遇零点血压计range ①范围，幅度②度盘，标度range-finder 测距器range indicator 距离指示器range of accommodation 调节幅度range of audibility 可听范围range of vision 视力范围ranger 测距仪rank 排列，分类，序列rankine's apparatus 兰金氏气体粘度计rapid film 快速软片rapid perforation awl 快速钻颅用穿刺锥rare 稀有的，珍贵的rare-earth intensifying screen 稀土元素增感屏rasion 锉刮，锉磨（用锉刀锉磨药物）rasp 锉raspatory 骨锉，骨刮raster 光栅，屏面ratch/ratlat ratchet 棘轮。
量子力学教程（第三版）周世勋课后答案详解高等教育出版社.pdf
1量子力学课后习题详解第一章量子理论基础1．1由黑体辐射公式导出维恩位移定律：能量密度极大值所对应的波长m λ与温度T 成反比，即m λT=b （常量）；并近似计算b 的数值，准确到二位有效数字。
解根据普朗克的黑体辐射公式dv ec hvd kThv vv 11833−⋅=πρ，（1）以及c v =λ，（2）λρρd dv v v −=，（3）有,118)()(5−⋅=⋅=⎟⎠⎞⎜⎝⎛−=−=kT hcv v e hc cd c d d dv λλλπλλρλλλρλρρ这里的λρ的物理意义是黑体内波长介于λ与λ+d λ之间的辐射能量密度。
本题关注的是λ取何值时，λρ取得极大值，因此，就得要求λρ对λ的一阶导数为零，由此可求得相应的λ的值，记作m λ。
但要注意的是，还需要验证λρ对λ的二阶导数在m λ处的取值是否小于零，如果小于零，那么前面求得的m λ就是要求的，具体如下：201151186'=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−⋅+−−⋅=−kThc kThce kT hc ehc λλλλλπρ⇒115=−⋅+−−kThc ekThc λλ⇒kThc ekThc λλ=−−)1(5如果令x=kThcλ，则上述方程为xe x =−−)1(5这是一个超越方程。
首先，易知此方程有解：x=0，但经过验证，此解是平庸的；另外的一个解可以通过逐步近似法或者数值计算法获得：x=4.97，经过验证，此解正是所要求的，这样则有xkhc T m =λ把x 以及三个物理常量代入到上式便知Km T m ⋅×=−3109.2λ这便是维恩位移定律。
据此，我们知识物体温度升高的话，辐射的能量分布的峰值向较短波长方面移动，这样便会根据热物体（如遥远星体）的发光颜色来判定温度的高低。
1．2在0K 附近，钠的价电子能量约为3eV ，求其德布罗意波长。
解根据德布罗意波粒二象性的关系，可知E=hv ，λh P =如果所考虑的粒子是非相对论性的电子（2c E e µ<<动），那么ep E µ22=如果我们考察的是相对性的光子，那么E=pc注意到本题所考虑的钠的价电子的动能仅为3eV ，远远小于电子的质量与光速平方的乘积，即eV 61051.0×，因此利用非相对论性的电子的能量——动量关系式，这样，便有ph=λ3nmm mE c hc E h e e 71.01071.031051.021024.1229662=×=××××===−−µµ在这里，利用了meV hc ⋅×=−61024.1以及eVc e 621051.0×=µ最后，对Ec hc e 22µλ=作一点讨论，从上式可以看出，当粒子的质量越大时，这个粒子的波长就越短，因而这个粒子的波动性较弱，而粒子性较强；同样的，当粒子的动能越大时，这个粒子的波长就越短，因而这个粒子的波动性较弱，而粒子性较强，由于宏观世界的物体质量普遍很大，因而波动性极弱，显现出来的都是粒子性，这种波粒二象性，从某种子意义来说，只有在微观世界才能显现。
量子力学教程(第三版)周世勋课后答案详解
1量子力学课后习题详解第一章量子理论基础1．1由黑体辐射公式导出维恩位移定律：能量密度极大值所对应的波长m λ与温度T 成反比，即m λT=b （常量）；并近似计算b 的数值，准确到二位有效数字。
解根据普朗克的黑体辐射公式dv ec hvd kThv vv 11833−⋅=πρ，（1）以及c v =λ，（2）λρρd dv v v −=，（3）有,118)()(5−⋅=⋅=⎟⎠⎞⎜⎝⎛−=−=kT hcv v e hc cd c d d dv λλλπλλρλλλρλρρ这里的λρ的物理意义是黑体内波长介于λ与λ+d λ之间的辐射能量密度。
本题关注的是λ取何值时，λρ取得极大值，因此，就得要求λρ对λ的一阶导数为零，由此可求得相应的λ的值，记作m λ。
但要注意的是，还需要验证λρ对λ的二阶导数在m λ处的取值是否小于零，如果小于零，那么前面求得的m λ就是要求的，具体如下：201151186'=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−⋅+−−⋅=−kThc kThce kT hc ehc λλλλλπρ⇒115=−⋅+−−kThc ekThc λλ⇒kThc ekThc λλ=−−)1(5如果令x=kThcλ，则上述方程为xe x =−−)1(5这是一个超越方程。
首先，易知此方程有解：x=0，但经过验证，此解是平庸的；另外的一个解可以通过逐步近似法或者数值计算法获得：x=4.97，经过验证，此解正是所要求的，这样则有xkhc T m =λ把x 以及三个物理常量代入到上式便知Km T m ⋅×=−3109.2λ这便是维恩位移定律。
据此，我们知识物体温度升高的话，辐射的能量分布的峰值向较短波长方面移动，这样便会根据热物体（如遥远星体）的发光颜色来判定温度的高低。
1．2在0K 附近，钠的价电子能量约为3eV ，求其德布罗意波长。
解根据德布罗意波粒二象性的关系，可知E=hv ，λh P =如果所考虑的粒子是非相对论性的电子（2c E e µ<<动），那么ep E µ22=如果我们考察的是相对性的光子，那么E=pc注意到本题所考虑的钠的价电子的动能仅为3eV ，远远小于电子的质量与光速平方的乘积，即eV 61051.0×，因此利用非相对论性的电子的能量——动量关系式，这样，便有ph=λ3nmm mE c hc E h e e 71.01071.031051.021024.1229662=×=××××===−−µµ在这里，利用了meV hc ⋅×=−61024.1以及eVc e 621051.0×=µ最后，对Ec hc e 22µλ=作一点讨论，从上式可以看出，当粒子的质量越大时，这个粒子的波长就越短，因而这个粒子的波动性较弱，而粒子性较强；同样的，当粒子的动能越大时，这个粒子的波长就越短，因而这个粒子的波动性较弱，而粒子性较强，由于宏观世界的物体质量普遍很大，因而波动性极弱，显现出来的都是粒子性，这种波粒二象性，从某种子意义来说，只有在微观世界才能显现。
量子物理的读后感
量子物理的读后感（中英文实用版）Quantum physics, a realm where the impossible is possible, has intrigued me deeply after immersing myself in its study.The laws that govern our macro-world seem to lose their footing in this micro-world, where particles can be in two places at once and the very act of observation changes reality.It"s a humbling and awe-inspiring journey into the unknown, challenging our perceptions of existence and the nature of reality.量子物理，这个将不可能变为可能的领域，在深入阅读之后深深吸引了我。
在这个微观世界中，支配我们宏观世界的法则似乎失去了立足点，粒子可以同时存在于两个地方，而观察本身就能改变现实。
这是一段令人敬畏且充满未知的旅程，它挑战了我们对存在和现实本质的认知。
The book I read, "Quantum Physics for Dummies," simplified complex theories into relatable concepts, allowing me to grasp the basics without feeling overwhelmed.It"s fascinating how quantum entanglement defies the speed of light, connecting particles in an instant across vast distances, making me question our limited understanding of space and time.我所阅读的《量子物理傻瓜书》将复杂的理论简化成了容易理解的概念，让我能够在不感到困惑的情况下掌握基础知识。
量子力学第二版周世勋1PDF
1 Quantum mechanism Quantum mechanism 宝鸡文理学院物理与信息技术系1.《量子力学教程》曾谨言著 科学出版社2003年第一版 普通高等教育十五国家级规划教材 2.《量子力学导论》曾谨言著 北京大学出版社 1998年第二版 3.《量子力学导论》熊钰庆主编 广东高等教育出版社 2000年第一版 《量子力学教程》周世勋编 高等教育出版社参考书及学习网站4.《量子力学基础》关洪 高等教育出版社 1999年第一版 5.《量子力学》汪德新 湖北科学技术出版社出版 2000年第一版 6.《量子力学教程习题剖析》孙婷雅编 科学出版社出版 2004年第一版 7. 宝鸡文理学院陕西省精品课程《量子力学》http://218.195.112.45/jpkc/liangzi/kc_web/ Content Content 第一章绪论Ch1. The basic concepts of quantum mechanism 第二章波函数和薛定谔方程Ch2. The wave function and Schr??dinger’s equation 第三章量子力学中的力学量Ch3. The Dynamical variable in Quantum Mechanism 第四章态和力学量的表象Ch4. The representation of the states and operators 第五章微扰理论Ch5. Perturbation theory第六章散射Ch6. The general theory of scattering 第七章自旋与全同粒子Ch7. Spin and identity of particles The birth of quantum mechanismThe birth of quantum mechanism Chap.1.绪论The birth of quantum mechanism Chap.1.绪论The birth of quantum mechanism 6 1.1 经典物理学的困难The difficult in classical physics 1.2 光的波粒二象性The duality of light between wave and particle 1.3 微粒的波粒二象性The duality of small particles between wave and particle Chap.1.绪论The birth of quantum mechanism Chap.1.绪论The birth of quantum mechanism 7 近几十年来 在不同领域相继发现了宏观量子效应 如超导现象 超流现象 乃至一些天体现象表明宏观世界的物质运动也遵循量子力学规律 人们所熟知的经典力学规律只是量子力学规律在特定条件下的一个近似。
大学物理第13章 量子物理
5
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能量子概念的提出标志了量子力学的诞生，普 朗克为此获得1918年诺贝尔物理学奖。
2. 黑体辐射的两个定律： 斯特藩 — 玻耳兹曼定律
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大学物理英文版
§1-1 Frame of Reference Particle(质点）
1. Frame of Reference（参照系）
•张达宋 《物理学基本教程》 •李行一等， 《物理学基本教程教学参考书》 •李行一等，《物理学基本教程》习题分析与解答 •张三慧等， 《大学物理学》 •Halliday et.al 《Fundamentals of Physics》 •W. Sears et.al 《University Physics》 •史蒂芬.霍金，《时间简史》 •盛正卯等，《物理学与人类文明》 •B.K.里德雷，《时间、空间和万物》 •…………..
4.Units(单位）
International System of Units(SI: Syst me International d’Unit s 法语） is used in China
mass
m
kg:千克 kilogram
length
L m:米 meter
Time
t s:秒 second
5. Scalar and vector（标量和矢量）: Two types of physical quantities（量）:
教 学基本 要 求
1. 理解描述质点运动物理量的定义及其矢量性、相 对性和瞬时性； 2. 掌握运动方程的物理意义，会用微积分方法求解 运动学两类问题； 3. 掌握平面抛体运动和圆周运动的规律； 4. 理解运动描述的相对性，会用速度合成定理和加 速度合成定理解题。
重要历史人物
大学物理量子物理ppt
4．维恩位移律(经验公式) m = C T C = 5.880×1010 Hz/K
5．理论与实验的 对比
热力学和麦克斯韦分布率 经典电磁学和能量均分定理
经典物理学 遇到的困难
三. 普朗克的黑体辐射公式和能量子假说
量子物理（Quantum Physics）基础
引言 量子理论的诞生
经典物理理论完美的形式和预言的正确性： 1 牛顿力学预言海王星 2 热学与分子运动论 3 波动光学的成就 4 麦克斯韦电磁理论对电磁波的预言
……
“物理学的大厦已基本建成，后辈物理学家只要 做些修补工作就行了”。
著名的英国物理学家J.J.汤姆孙
r
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光电池 要么接收到, 要么没有
用粒子性可正确的解释，而不与实验发生矛盾
球面波强度 1/r2 ?
这里经典理论是错的
发射大量光子时, 经典理论是正确的
波列的概念与光的粒子性对应起来容易, 但不同
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第一章 波粒二象性（Duality）
§1 黑体辐射 §2 光电效应 §3 光的波粒二象性 光子 §4 康普顿散射 §5 实物粒子的波动性 §6 概率波和概率幅
§7 不确定关系
§1 黑体辐射 Black Body Radiation
一. 基本概念 1. 热辐射 Thermal Radiation
三.爱因斯坦的光量子论
继承和发展普朗克光量子假定
天体物理硕士点培养方案修改草稿
天体物理硕士点培养方案修改草稿一、培养目标掌握坚实的理论物理基础和系统的专门知识，熟悉理论物理专业有关方向的国内外研究历史、现状和发展方向，掌握一门外语，具有从事科学研究、高等学校教学工作或独立担负有关专门技术工作能力，成为德智体全面发展，适应社会主义现代化需要的高层次人才。
二、研究方向1、核与粒子天体物理2、高能天体物理3、相对论天体物理三、学习年限与学分天体物理专业修年限为2至3年。
总学分为36-40学分四、课程设置（一）学位课程（本专业各方向向硕士生公共必修课，计27学分）（二）指定选修课（按研究方向设置）（三）任意选修课五、教学实践天体物理专业硕士生的教学实践，一般安排在第二学年。
内容是协助本专业主讲教师为本科生课程及低年级的学士学位专业主干课作辅导答疑；主持习题课；指导实验课；和协助指导本科生论文写作。
六、调查研究本专业调查研究定为2周，一般在第二学年初进行。
主要以到大型图书馆、国内资料中心调研各自研究方向的历史、现状和发展动向，以及进行课题调研。
应写出调研报告。
七、科学研究及学位论文要求1、本专业硕士生在校期间应至少完成1篇课程论文，2篇学术论文达到期刊发表的水平，其中应至少有一篇在国内核心刊物公开发表。
2、本专业硕士生至迟应在第四学期中确定学位论文题目，通过学位论文开题报告，并订出学位论文工作计划，论文开题报告一般定在第五学期。
3、本专业硕士生学位论文选题及学术要求为：（1）学术性。
研究天体物理学当前关注的有意义的课题，致力于解决其中的某个或一部分问题。
（2）新颖性。
提出有新意的理论思想，或按照基本理论对物理现象伤作出新的解释，或建立有新特点的研究方法。
（3）工作量。
论文应在反映硕士生有大约一年时间致力于学位论文相关的工作。
（4））全面性。
较全面地对硕士生的综合能力作训练。
八、培养方式与方法采取理论学习和科研相结合，导师指导和课题小组集体指导、培养相结合，经常参加国内学术交流会议，充分发挥导师的主导作用和研究生的主动性，以灵活的方法，着力培养研究一的科研能力和独立工作能力，并力求进取和创新。
量子力学答案课后 习题答案详解(周世勋)
量子力学习题及解答第一章 量子理论基础1．1。
解 根据普朗克的黑体辐射公式dv echv d kThv v v 11833-⋅=πρ， 以及 c v =λ， （2）λρρd dv v v -=， （3）有,118)()(5-⋅=⋅=⎪⎭⎫ ⎝⎛-=-=kThc v v ehc cd c d d dv λλλπλλρλλλρλρρ这里的λρ的物理意义是黑体内波长介于λ与λ+d λ之间的辐射能量密度。
本题关注的是λ取何值时，λρ取得极大值，因此，就得要求λρ 对λ的一阶导数为零，由此可求得相应的λ的值，记作m λ。
但要注意的是，还需要验证λρ对λ的二阶导数在m λ处的取值是否小于零，如果小于零，那么前面求得的m λ就是要求的，具体如下：01151186'=⎪⎪⎪⎭⎫⎝⎛-⋅+--⋅=-kT hc kThc e kT hc ehcλλλλλπρ ⇒ 0115=-⋅+--kThc ekThcλλ⇒ kThcekThcλλ=--)1(5 如果令x=kThcλ ，则上述方程为 x e x =--)1(5这是一个超越方程。
首先，易知此方程有解：x=0，但经过验证，此解是平庸的；另外的一个解可以通过逐步近似法或者数值计算法获得：x=4.97，经过验证，此解正是所要求的，这样则有xkhc T m =λ 把x 以及三个物理常量代入到上式便知K m T m ⋅⨯=-3109.2λ这便是维恩位移定律。
据此，我们知识物体温度升高的话，辐射的能量分布的峰值向较短波长方面移动，这样便会根据热物体（如遥远星体）的发光颜色来判定温度的高低。
1．2 解 根据德布罗意波粒二象性的关系，可知E=hv ，λhP =如果所考虑的粒子是非相对论性的电子（2c E e μ<<动），那么ep E μ22= 如果我们考察的是相对性的光子，那么E=pc注意到本题所考虑的钠的价电子的动能仅为3eV ，远远小于电子的质量与光速平方的乘积，即eV 61051.0⨯，因此利用非相对论性的电子的能量——动量关系式，这样，便有ph =λ nmm m E c hc E h e e 71.01071.031051.021024.1229662=⨯=⨯⨯⨯⨯===--μμ在这里，利用了m eV hc ⋅⨯=-61024.1以及eV c e 621051.0⨯=μ最后，对Ec hc e 22μλ=作一点讨论，从上式可以看出，当粒子的质量越大时，这个粒子的波长就越短，因而这个粒子的波动性较弱，而粒子性较强；同样的，当粒子的动能越大时，这个粒子的波长就越短，因而这个粒子的波动性较弱，而粒子性较强，由于宏观世界的物体质量普遍很大，因而波动性极弱，显现出来的都是粒子性，这种波粒二象性，从某种子意义来说，只有在微观世界才能显现。
量子信息——连续变量篇
Quantum information with continuous variablesSamuel L.BraunsteinComputer Science,University of York,York YO105DD,United KingdomPeter van LoockNational Institute of Informatics(NII),Tokyo101-8430,Japan and Institute of TheoreticalPhysics,Institute of Optics,Information and Photonics(Max-Planck Forschungsgruppe),Universität Erlangen-Nürnberg,D-91058Erlangen,Germany͑Published29June2005͒Quantum information is a rapidly advancing area of interdisciplinary research.It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement.This article reviews the progress in quantum information based on continuous quantum variables,with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagneticfield.CONTENTSI.Introduction513II.Continuous Variables in Quantum Optics516A.The quadratures of the quantizedfield516B.Phase-space representations518C.Gaussian states519D.Linear optics519E.Nonlinear optics520F.Polarization and spin representations522G.Necessity of phase reference523 III.Continuous-Variable Entanglement523A.Bipartite entanglement5251.Pure states5252.Mixed states and inseparability criteria526B.Multipartite entanglement5291.Discrete variables5292.Genuine multipartite entanglement5303.Separability properties of Gaussian states5304.Generating entanglement5315.Measuring entanglement533C.Bound entanglement534D.Nonlocality5341.Traditional EPR-type approach5352.Phase-space approach5363.Pseudospin approach536E.Verifying entanglement experimentally537 IV.Quantum Communication with Continuous Variables538A.Quantum teleportation5401.Teleportation protocol5412.Teleportation criteria5433.Entanglement swapping546B.Dense coding546rmation:A measure5472.Mutual information5473.Classical communication5474.Classical communication via quantum states5475.Dense coding548C.Quantum error correction550D.Quantum cryptography5501.Entanglement-based versus prepare andmeasure5502.Early ideas and recent progress5513.Absolute theoretical security5524.Verifying experimental security5535.Quantum secret sharing553E.Entanglement distillation554F.Quantum memory555V.Quantum Cloning with Continuous Variables555A.Local universal cloning5551.Beyond no-cloning5552.Universal cloners556B.Local cloning of Gaussian states5571.Fidelity bounds for Gaussian cloners5572.An optical cloning circuit for coherentstates558C.Telecloning559 VI.Quantum Computation with Continuous Variables560A.Universal quantum computation560B.Extension of the Gottesman-Knill theorem563 VII.Experiments with Continuous Quantum Variables565A.Generation of squeezed-state EPR entanglement5651.Broadband entanglement via opticalparametric amplification5652.Kerr effect and linear interference567B.Generation of long-lived atomic entanglement568C.Generation of genuine multipartite entanglement569D.Quantum teleportation of coherent states569E.Experimental dense coding570F.Experimental quantum key distribution571G.Demonstration of a quantum memory effect572 VIII.Concluding Remarks572 Acknowledgments573 References573I.INTRODUCTIONQuantum information is a relatively young branch of physics.One of its goals is to interpret the concepts of quantum physics from an information-theoretic point of view.This may lead to a deeper understanding of quan-REVIEWS OF MODERN PHYSICS,VOLUME77,APRIL20050034-6861/2005/77͑2͒/513͑65͒/$50.00©2005The American Physical Society513tum theory.Conversely,information and computation are intrinsically physical concepts,since they rely on physical systems in which information is stored and by means of which information is processed or transmitted. Hence physical concepts,and at a more fundamental level quantum physical concepts,must be incorporated in a theory of information and computation.Further-more,the exploitation of quantum effects may even prove beneficial for various kinds of information pro-cessing and communication.The most prominent ex-amples of this are quantum computation and quantum key distribution.Quantum computation means in par-ticular cases,in principle,computation faster than any known classical computation.Quantum key distribution makes possible,in principle,unconditionally secure communication as opposed to communication based on classical key distribution.From a conceptual point of view,it is illuminating to consider continuous quantum variables in quantum in-formation theory.This includes the extension of quan-tum communication protocols from discrete to continu-ous variables and hence fromfinite to infinite dimensions.For instance,the original discrete-variable quantum teleportation protocol for qubits and other finite-dimensional systems͑Bennett et al.,1993͒was soon after its publication translated into the continuous-variable setting͑Vaidman,1994͒.The main motivation for dealing with continuous variables in quantum infor-mation,however,originated in a more practical observa-tion:efficient implementation of the essential steps in quantum communication protocols,namely,preparing, unitarily manipulating,and measuring͑entangled͒quan-tum states,is achievable in quantum optics utilizing con-tinuous quadrature amplitudes of the quantized electro-magneticfield.For example,the tools for measuring a quadrature with near-unit efficiency or for displacing an optical mode in phase space are provided by homodyne-detection and feedforward techniques,respectively. Continuous-variable entanglement can be efficiently produced using squeezed light͓in which the squeezing of a quadrature’s quantumfluctuations is due to a non-linear optical interaction͑Walls and Milburn,1994͔͒and linear optics.A valuable feature of quantum optical implementa-tions based upon continuous variables,related to their high efficiency,is their unconditionalness.Quantum re-sources such as entangled states emerge from the non-linear optical interaction of a laser with a crystal͑supple-mented if necessary by some linear optics͒in an unconditional fashion,i.e.,every inverse bandwidth time.This unconditionalness is hard to obtain in discrete-variable qubit-based implementations using single-photon states.In that case,the desired prepara-tion due to the nonlinear optical interaction depends on particular͑coincidence͒measurement results ruling out the unwanted͑in particular,vacuum͒contributions in the outgoing state vector.However,the unconditional-ness of the continuous-variable implementations has its price:it is at the expense of the quality of the entangle-ment of the prepared states.This entanglement and hence any entanglement-based quantum protocol is al-ways imperfect,the degree of imperfection depending on the amount of squeezing of the laser light involved. Good quality and performance require large squeezing which is technologically demanding,but to a certain ex-tent͓about10dB͑Wu et al.,1986͔͒already state of the art.Of course,in continuous-variable protocols that do not rely on entanglement,for instance,coherent-state-based quantum key distribution,these imperfections do not occur.To summarize,in the most commonly used optical ap-proaches,the continuous-variable implementations al-ways work pretty well͑and hence efficiently and uncon-ditionally͒,but never perfectly.Their discrete-variable counterparts only work sometimes͑conditioned upon rare successful events͒,but they succeed,in principle, perfectly.A similar tradeoff occurs when optical quan-tum states are sent through noisy channels͑opticalfi-bers͒,for example,in a realistic quantum key distribu-tion scenario.Subject to losses,the continuous-variable states accumulate noise and emerge at the receiver as contaminated versions of the sender’s input states.The discrete-variable quantum information encoded in single-photon states is reliably conveyed for each photon that is not absorbed during transmission.Due to the recent results of Knill,Laflamme,and Mil-burn͑Knill et al.,2001͒,it is now known that efficient quantum information processing is possible,in principle, solely by means of linear optics.Their scheme is formu-lated in a discrete-variable setting in which the quantum information is encoded in single-photon states.Apart from entangled auxiliary photon states,generated off-line without restriction to linear optics,conditional dy-namics͑feedforward͒is the essential ingredient in mak-ing this approach work.Universal quantum gates such as a controlled-NOT gate can,in principle,be built using this scheme without need of any Kerr-type nonlinear op-tical interaction͑corresponding to an interaction Hamil-tonian quartic in the optical modes’annihilation and creation operators͒.This Kerr-type interaction would be hard to obtain on the level of single photons.However, the off-line generation of the complicated auxiliary states needed in the Knill-Laflamme-Milburn scheme seems impractical too.Similarly,in the continuous-variable setting,when it comes to more advanced quantum information proto-cols,such as universal quantum computation or,in a communication scenario,entanglement distillation,it turns out that tools more sophisticated than mere Gaussian operations are needed.In fact,the Gaussian operations are effectively those described by interaction Hamiltonians at most quadratic in the optical modes’annihilation and creation operators,thus leading to lin-ear input-output relations as in beam-splitter or squeez-ing transformations.Gaussian operations,mapping Gaussian states onto Gaussian states,also include ho-modyne detections and phase-space displacements.In contrast,the non-Gaussian operations required for ad-vanced continuous-variable quantum communication͑in particular,long-distance communication based on en-514S.L.Braunstein and P.van Loock:Quantum information with continuous variables Rev.Mod.Phys.,Vol.77,No.2,April2005tanglement distillation and swapping,quantum memory,and teleportation͒are due either to at least cubic non-linear optical interactions or to conditional transforma-tions depending on non-Gaussian measurements such asphoton counting.It seems that,at this very sophisticatedlevel,the difficulties and requirements of the discrete-and continuous-variable implementations are analogous.In this review,our aim is to highlight the strengths ofthe continuous-variable approaches to quantum infor-mation processing.Therefore we focus on those proto-cols that are based on Gaussian states and their feasiblemanipulation through Gaussian operations.This leads tocontinuous-variable proposals for the implementation ofthe simplest quantum communication protocols,such asquantum teleportation and quantum key distribution,and includes the efficient generation and detection ofcontinuous-variable entanglement.Before dealing with quantum communication andcomputation,in Sec.II,wefirst introduce continuousquantum variables within the framework of quantumoptics.The discussions about the quadratures of quan-tized electromagnetic modes,about phase-space repre-sentations,and about Gaussian states include the nota-tions and conventions that we use throughout thisarticle.We conclude Sec.II with a few remarks on linearand nonlinear optics,on alternative polarization andspin representations,and on the necessity of a phasereference in continuous-variable implementations.Thenotion of entanglement,indispensable in many quantumprotocols,is described in Sec.III in the context of con-tinuous variables.We discuss pure and mixed entangledstates,entanglement between two͑bipartite͒and be-tween many͑multipartite͒parties,and so-called bound ͑undistillable͒entanglement.The generation,measure-ment,and verification͑both theoretical and experimen-tal͒of continuous-variable entanglement are here of par-ticular interest.As for the properties of the continuous-variable entangled states related with theirinseparability,we explain how the nonlocal character ofthese states is revealed.This involves,for instance,vio-lations of Bell-type inequalities imposed by local real-ism.Such violations,however,cannot occur when themeasurements considered are exclusively of continuous-variable type.This is due to the strict positivity of theWigner function of the Gaussian continuous-variable en-tangled states,which allows for a hidden-variable de-scription in terms of the quadrature observables.In Sec.IV,we describe the conceptually and practi-cally most important quantum communication protocols formulated in terms of continuous variables and thus utilizing the continuous-variable͑entangled͒states. These schemes include quantum teleportation and en-tanglement swapping͑teleportation of entanglement͒, quantum͑super͒dense coding,quantum error correc-tion,quantum cryptography,and entanglement distilla-tion.Since quantum teleportation based on nonmaxi-mum continuous-variable entanglement,usingfinitely squeezed two-mode squeezed states,is always imperfect, teleportation criteria are needed both for the theoretical and for the experimental verification.As is known from classical communication,light,propagating at high speed and offering a broad range of different frequen-cies,is an ideal carrier for the transmission of informa-tion.This applies to quantum communication as well. However,light is less suited for the storage of informa-tion.In order to store quantum information,for in-stance,at the intermediate stations in a quantum re-peater,atoms are more appropriate media than light. Significantly,as another motivation to deal with continu-ous variables,a feasible light-atom interface can be built via free-space interaction of light with an atomic en-semble based on the alternative polarization and spin-type variables.No strong cavity QED coupling is needed as with single photons.The concepts of this transfer of quantum information from light to atoms and vice versa, as the essential ingredients of a quantum memory,are discussed in Sec.IV.FSection V is devoted to quantum cloning with con-tinuous variables.One of the most fundamental͑and historically one of thefirst͒“laws”of quantum informa-tion theory is the so-called no-cloning theorem͑Dieks, 1982;Wootters and Zurek,1982͒.It forbids the exact copying of arbitrary quantum states.However,arbitrary quantum states can be copied approximately,and the resemblance͑in mathematical terms,the overlap orfi-delity͒between the clones may attain an optimal value independent of the original states.Such optimal cloning can be accomplished locally by sending the original states͑together with some auxiliary system͒through a local unitary quantum circuit.Optimal cloning of Gauss-ian continuous-variable states appears to be more inter-esting than that of general continuous-variable states, because the latter can be mimicked by a simple coin toss.We describe a non-entanglement-based implemen-tation for the optimal local cloning of Gaussian continuous-variable states.In addition,for Gaussian continuous-variable states,an optical implementation exists of optimal cloning at a distance͑telecloning͒.In this case,the optimality requires entanglement.The cor-responding multiparty entanglement is again producible with nonlinear optics͑squeezed light͒and linear optics ͑beam splitters͒.Quantum computation over continuous variables,dis-cussed in Sec.VI,is a more subtle issue than the in some sense straightforward continuous-variable extensions of quantum communication protocols.Atfirst sight,con-tinuous variables do not appear well suited for the pro-cessing of digital information in a computation.On the other hand,a continuous-variable quantum state having an infinite-dimensional spectrum of eigenstates contains a vast amount of quantum information.Hence it might be promising to adjust the continuous-variable states theoretically to the task of computation͑for instance,by discretization͒and yet to exploit their continuous-variable character experimentally in efficient͑optical͒implementations.We explain in Sec.VI why universal quantum computation over continuous variables re-quires Hamiltonians at least cubic in the position and momentum͑quadrature͒operators.Similarly,any quan-tum circuit that consists exclusively of unitary gates from515S.L.Braunstein and P.van Loock:Quantum information with continuous variables Rev.Mod.Phys.,Vol.77,No.2,April2005the continuous-variable Clifford group can be efficientlysimulated by purely classical means.This is acontinuous-variable extension of the discrete-variableGottesman-Knill theorem in which the Clifford groupelements include gates such as the Hadamard͑in thecontinuous-variable case,Fourier͒transform or the con-trolled NOT͑CNOT͒.The theorem applies,for example,to quantum teleportation which is fully describable by CNOT’s and Hadamard͑or Fourier͒transforms of some eigenstates supplemented by measurements in thateigenbasis and spin or phaseflip operations͑or phase-space displacements͒.Before some concluding remarks in Sec.VIII,wepresent some of the experimental approaches to squeez-ing of light and squeezed-state entanglement generationin Sec.VII.A.Both quadratic and quartic optical nonlin-earities are suitable for this,namely,parametric downconversion and the Kerr effect,respectively.Quantumteleportation experiments that have been performed al-ready based on continuous-variable squeezed-state en-tanglement are described in Sec.VII.D.In Sec.VII,wefurther discuss experiments with long-lived atomic en-tanglement,with genuine multipartite entanglement ofoptical modes,experimental dense coding,experimentalquantum key distribution,and the demonstration of aquantum memory effect.II.CONTINUOUS VARIABLES IN QUANTUM OPTICSFor the transition from classical to quantum mechan-ics,the position and momentum observables of the par-ticles turn into noncommuting Hermitian operators inthe Hamiltonian.In quantum optics,the quantized elec-tromagnetic modes correspond to quantum harmonicoscillators.The modes’quadratures play the roles of theoscillators’position and momentum operators obeyingan analogous Heisenberg uncertainty relation.A.The quadratures of the quantizedfieldFrom the Hamiltonian of a quantum harmonic oscil-lator expressed in terms of͑dimensionless͒creation and annihilation operators and representing a single mode k, Hˆk=បk͑aˆk†aˆk+12͒,we obtain the well-known form writ-ten in terms of“position”and“momentum”operators ͑unit mass͒,Hˆk=12͑pˆk2+k2xˆk2͒,͑1͒withaˆk=1ͱ2បk͑k xˆk+ipˆk͒,͑2͒aˆk†=1ͱ2បk͑k xˆk−ipˆk͒,͑3͒or,conversely,xˆk=ͱប2k͑aˆk+aˆk†͒,͑4͒pˆk=−iͱបk2͑aˆk−aˆk†͒.͑5͒Here,we have used the well-known commutation rela-tion for position and momentum,͓xˆk,pˆkЈ͔=iប␦kkЈ,͑6͒which is consistent with the bosonic commutation rela-tions͓aˆk,aˆkЈ†͔=␦kkЈ,͓aˆk,aˆkЈ͔=0.In Eq.͑2͒,we see that up to normalization factors the position and the momentum are the real and imaginary parts of the annihilation op-erator.Let us now define the dimensionless pair of con-jugate variables,Xˆkϵͱk2បxˆk=Re aˆk,Pˆkϵ1ͱ2បk pˆk=Im aˆk.͑7͒Their commutation relation is then͓Xˆk,PˆkЈ͔=i2␦kkЈ.͑8͒In other words,the dimensionless position and momen-tum operators,Xˆk and Pˆk,are defined as if we setប=1/2.These operators represent the quadratures of a single mode k,in classical terms corresponding to the real and imaginary parts of the oscillator’s complex am-plitude.In the following,by using͑Xˆ,Pˆ͒or equivalently ͑xˆ,pˆ͒,we shall always refer to these dimensionless quadratures as playing the roles of position and momen-tum.Hence͑xˆ,pˆ͒will also stand for a conjugate pair of dimensionless quadratures.The Heisenberg uncertainty relation,expressed in terms of the variances of two arbitrary noncommuting observables Aˆand Bˆfor an arbitrary given quantum state,͗͑⌬Aˆ͒2͘ϵŠ͑Aˆ−͗Aˆ͒͘2‹=͗Aˆ2͘−͗Aˆ͘2,͗͑⌬Bˆ͒2͘ϵŠ͑Bˆ−͗Bˆ͒͘2‹=͗Bˆ2͘−͗Bˆ͘2,͑9͒becomes͗͑⌬Aˆ͒2͗͑͘⌬Bˆ͒2͘ജ14͉͓͗Aˆ,Bˆ͔͉͘2.͑10͒Inserting Eq.͑8͒into Eq.͑10͒yields the uncertainty re-lation for a pair of conjugate quadrature observables of a single mode k,xˆk=͑aˆk+aˆk†͒/2,pˆk=͑aˆk−aˆk†͒/2i,͑11͒namely,͗͑⌬xˆk͒2͗͑͘⌬pˆk͒2͘ജ14͉͓͗xˆk,pˆk͔͉͘2=116.͑12͒Thus,in our units,the quadrature variance for a vacuum or coherent state of a single mode is1/4.Let us further516S.L.Braunstein and P.van Loock:Quantum information with continuous variables Rev.Mod.Phys.,Vol.77,No.2,April2005illuminate the meaning of the quadratures by looking at a single frequency mode of the electric field ͑for a single polarization ͒,E ˆk ͑r ,t ͒=E 0͓a ˆk ei ͑k ·r −k t ͒+a ˆk †e −i ͑k ·r −k t ͔͒.͑13͒The constant E 0contains all the dimensional prefactors.By using Eq.͑11͒,we can rewrite the mode asE ˆk ͑r ,t ͒=2E 0͓x ˆk cos ͑k t −k ·r ͒+pˆk sin ͑k t −k ·r ͔͒.͑14͒Clearly,the position and momentum operators xˆk and p ˆk represent the in-phase and out-of-phase components of the electric-field amplitude of the single mode k with respect to a ͑classical ͒reference wave ϰcos ͑k t −k ·r ͒.The choice of the phase of this wave is arbitrary,of course,and a more general reference wave would lead us to the single-mode descriptionE ˆk ͑r ,t ͒=2E 0͓x ˆk ͑⌰͒cos ͑k t −k ·r −⌰͒+pˆk ͑⌰͒sin ͑k t −k ·r −⌰͔͒,͑15͒with the more general quadraturesxˆk ͑⌰͒=͑a ˆk e −i ⌰+a ˆk †e +i ⌰͒/2,͑16͒p ˆk ͑⌰͒=͑a ˆk e −i ⌰−a ˆk †e +i ⌰͒/2i .͑17͒These new quadratures can be obtained from x ˆk and p ˆk via the rotationͩx ˆk ͑⌰͒pˆk ͑⌰͒ͪ=ͩcos ⌰sin ⌰−sin ⌰cos ⌰ͪͩxˆk pˆk ͪ.͑18͒Since this is a unitary transformation,we again end upwith a pair of conjugate observables fulfilling the com-mutation relation ͑8͒.Furthermore,because pˆk ͑⌰͒=x ˆk ͑⌰+/2͒,the whole continuum of quadratures is cov-ered by x ˆk ͑⌰͒with ⌰͓0,͒.This continuum of observ-ables is indeed measurable by relatively simple means.Such a so-called homodyne detection works as follows.A photodetector measuring an electromagnetic mode converts the photons into electrons and hence into an electric current,called the photocurrent i ˆ.It is therefore sensible to assume i ˆϰn ˆ=a ˆ†a ˆor i ˆ=qaˆ†a ˆwhere q is a con-stant ͑Paul,1995͒.In order to detect a quadrature of themode aˆ,the mode must be combined with an intense local oscillator at a 50:50beam splitter.The local oscil-lator is assumed to be in a coherent state with large photon number,͉␣LO ͘.It is therefore reasonable to de-scribe this oscillator by a classical complex amplitude␣LO rather than by an annihilation operator aˆLO .The two output modes of the beam splitter,͑aˆLO +a ˆ͒/ͱ2and ͑a ˆLO −a ˆ͒/ͱ2͑see Sec.II.D ͒,may then be approximated byaˆ1=͑␣LO +a ˆ͒/ͱ2,aˆ2=͑␣LO −a ˆ͒/ͱ2.͑19͒This yields the photocurrentsi ˆ1=qa ˆ1†aˆ1=q ͑␣LO *+a ˆ†͒͑␣LO +a ˆ͒/2,i ˆ2=qa ˆ2†aˆ2=q ͑␣LO *−a ˆ†͒͑␣LO −a ˆ͒/2.͑20͒The actual quantity to be measured will be the differ-ence photocurrent␦i ˆϵi ˆ1−i ˆ2=q ͑␣LO *aˆ+␣LO a ˆ†͒.͑21͒By introducing the phase ⌰of the local oscillator,␣LO=͉␣LO ͉exp ͑i ⌰͒,we recognize that the quadrature observ-able xˆ͑⌰͒from Eq.͑16͒is measured ͑without mode index k ͒.Now adjustment of the local oscillator’s phase ⌰͓0,͔enables us to detect any quadrature from thewhole continuum of quadratures xˆ͑⌰͒.A possible way to realize quantum tomography ͑Leonhardt,1997͒,i.e.,the reconstruction of the mode’s quantum state given by its Wigner function,relies on this measurement method,called ͑balanced ͒homodyne detection .A broadband rather than a single-mode description of homodyne de-tection can be found in the work of Braunstein and Crouch ͑1991͒,who also investigate the influence of a quantized local oscillator.We have now seen that it is not too hard to measure the quadratures of an electromagnetic mode.Unitary transformations such as quadrature displacements ͑phase-space displacements ͒can also be relatively easily performed via the so-called feedforward technique,as opposed to,for example,photon number displacements.This simplicity and the high efficiency when measuring and manipulating continuous quadratures are the main reasons why continuous-variable schemes appear more attractive than those based on discrete variables such as the photon number.In the following,we shall refer mainly to the conju-gate pair of quadratures xˆk and p ˆk ͑position and momen-tum,i.e.,⌰=0and ⌰=/2͒.In terms of these quadra-tures,the number operator becomesn ˆk =a ˆk †a ˆk =x ˆk 2+p ˆk 2−12,͑22͒using Eq.͑8͒.Let us finally review some useful formulas for the single-mode quadrature eigenstates,xˆ͉x ͘=x ͉x ͘,pˆ͉p ͘=p ͉p ͘,͑23͒where we have now dropped the mode index k .They are orthogonal,͗x ͉x Ј͘=␦͑x −x Ј͒,͗p ͉p Ј͘=␦͑p −p Ј͒,͑24͒and complete,͵−ϱϱ͉x ͗͘x ͉dx =1,͵−ϱϱ͉p ͗͘p ͉dp =1.͑25͒Just as for position and momentum eigenstates,the quadrature eigenstates are mutually related to each other by a Fourier transformation,͉x ͘=1ͱ͵−ϱϱe −2ixp ͉p ͘dp ,͑26͒517S.L.Braunstein and P .van Loock:Quantum information with continuous variablesRev.Mod.Phys.,Vol.77,No.2,April 2005͉p͘=1ͱ͵−ϱϱe+2ixp͉x͘dx.͑27͒Despite being unphysical and not square integrable,the quadrature eigenstates can be very useful in calculations involving the wave functions͑x͒=͗x͉͘,etc.,and inidealized quantum communication protocols based on continuous variables.For instance,a vacuum state infi-nitely squeezed in position may be expressed by a zero-position eigenstate͉x=0͘=͉͐p͘dp/ͱ.The physical,fi-nitely squeezed states are characterized by the quadrature probability distributions͉͑x͉͒2,etc.,ofwhich the widths correspond to the quadrature uncer-tainties.B.Phase-space representationsThe Wigner function is particularly suitable as a “quantum phase-space distribution”for describing the effects on the quadrature observables that may arise from quantum theory and classical statistics.It behaves partly as a classical probability distribution,thus en-abling us to calculate measurable quantities such as mean values and variances of the quadratures in a classical-like fashion.On the other hand,in contrast to a classical probability distribution,the Wigner function can become negative.The Wigner function was originally proposed by Wigner in his1932paper“On the quantum correction for thermodynamic equilibrium”͑Wigner,1932͒.There, he gave an expression for the Wigner function in terms of the position basis which reads͑with x and p being a dimensionless pair of quadratures in our units withប=1/2as introduced in the previous section;Wigner, 1932͒W͑x,p͒=2͵dye+4iyp͗x−y͉ˆ͉x+y͘.͑28͒Here and throughout,unless otherwise specified,the in-tegration will be over the entire space of the integration variable͑i.e.,here the integration goes from−ϱtoϱ͒. We gave Wigner’s original formula for only one mode or one particle͓Wigner’s͑1932͒original equation was in N-particle form͔because it simplifies the understanding of the concept behind the Wigner function approach. The extension to N modes is straightforward.Why does W͑x,p͒resemble a classical-like probability distribution?The most important attributes that explain this are the proper normalization,͵W͑␣͒d2␣=1,͑29͒the property of yielding the correct marginal distribu-tions,͵W͑x,p͒dx=͗p͉ˆ͉p͘,͵W͑x,p͒dp=͗x͉ˆ͉x͘,͑30͒and the equivalence to a probability distribution in clas-sical averaging when mean values of a certain class of operators Aˆin a quantum stateˆare to be calculated,͗Aˆ͘=Tr͑ˆAˆ͒=͵W͑␣͒A͑␣͒d2␣,͑31͒with a function A͑␣͒related to the operator Aˆ.The measure of integration is in our case d2␣=d͑Re␣͒d͑Im␣͒=dxdp with W͑␣=x+ip͒ϵW͑x,p͒,and we shall use d2␣and dxdp interchangeably.The opera-tor Aˆrepresents a particular class of functions of aˆand aˆ†or xˆand pˆ.The marginal distribution for p,͗p͉ˆ͉p͘,is obtained by changing the integration variables͑x−y =u,x+y=v͒and using Eq.͑26͒,that for x,͗x͉ˆ͉x͘,by using͐exp͑+4iyp͒dp=͑/2͒␦͑y͒.The normalization of the Wigner function then follows from Tr͑ˆ͒=1.For any symmetrized operator͑Leonhardt,1997͒,the so-called Weyl correspondence͑Weyl,1950͒,Tr͓ˆS͑xˆn pˆm͔͒=͵W͑x,p͒x n p m dxdp,͑32͒provides a rule for calculating quantum-mechanical ex-pectation values in a classical-like fashion according to Eq.͑31͒.Here,S͑xˆn pˆm͒indicates symmetrization.For example,S͑xˆ2pˆ͒=͑xˆ2pˆ+xˆpˆxˆ+pˆxˆ2͒/3corresponds to x2p ͑Leonhardt,1997͒.Such a classical-like formulation of quantum optics in terms of quasiprobability distributions is not unique.In fact,there is a whole family of distributions P͑␣,s͒of which each member corresponds to a particular value of a real parameter s,P͑␣,s͒=12͵͑,s͒exp͑i␣*+i*␣͒d2,͑33͒with the s-parametrized characteristic functions ͑,s͒=Tr͓ˆexp͑−iaˆ†−i*aˆ͔͒exp͑s͉͉2/2͒.͑34͒The mean values of operators normally and antinor-mally ordered in aˆand aˆ†may be calculated via the so-called P function͑s=1͒and Q function͑s=−1͒,re-spectively.The Wigner function͑s=0͒and its character-istic function͑,0͒are perfectly suited to provide ex-pectation values of quantities symmetric in aˆand aˆ†such as the quadratures.Hence the Wigner function,though not always positive definite,appears to be a good com-promise in describing quantum states in terms of quan-tum phase-space variables such as single-mode quadra-tures.We may formulate various quantum states relevant to continuous-variable quantum communica-tion by means of the Wigner representation.These par-ticular quantum states exhibit extremely nonclassical features such as entanglement and nonlocality.Yet their Wigner functions are positive definite,and thus belong to the class of Gaussian states.518S.L.Braunstein and P.van Loock:Quantum information with continuous variables Rev.Mod.Phys.,Vol.77,No.2,April2005。
周世勋量子力学习题及解答（ＰＤＦ）
量子力学习题及解答第一章量子理论基础1．1由黑体辐射公式导出维恩位移定律：能量密度极大值所对应的波长m λ与温度T 成反比，即m λT=b （常量）；并近似计算b 的数值，准确到二位有效数字。
解根据普朗克的黑体辐射公式dv e chv d kThv v v 11833−⋅=πρ，（1）以及c v =λ，（2）λρρd dv v v −=，（3）有,118)()(5−⋅=⋅=⎟⎠⎞⎜⎝⎛−=−=kT hc v v e hc cd c d d dv λλλπλλρλλλρλρρ这里的λρ的物理意义是黑体内波长介于λ与λ+d λ之间的辐射能量密度。
本题关注的是λ取何值时，λρ取得极大值，因此，就得要求λρ对λ的一阶导数为零，由此可求得相应的λ的值，记作m λ。
但要注意的是，还需要验证λρ对λ的二阶导数在m λ处的取值是否小于零，如果小于零，那么前面求得的m λ就是要求的，具体如下：01151186'=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−⋅+−−⋅=−kT hc kThc e kT hc ehc λλλλλπρ⇒0115=−⋅+−−kThc ekThc λλ⇒kThc ekThc λλ=−−)1(5如果令x=kThcλ，则上述方程为xe x =−−)1(5这是一个超越方程。
首先，易知此方程有解：x=0，但经过验证，此解是平庸的；另外的一个解可以通过逐步近似法或者数值计算法获得：x=4.97，经过验证，此解正是所要求的，这样则有xkhc T m =λ把x 以及三个物理常量代入到上式便知Km T m ⋅×=−3109.2λ这便是维恩位移定律。
据此，我们知识物体温度升高的话，辐射的能量分布的峰值向较短波长方面移动，这样便会根据热物体（如遥远星体）的发光颜色来判定温度的高低。
1．2在0K 附近，钠的价电子能量约为3eV ，求其德布罗意波长。
解根据德布罗意波粒二象性的关系，可知E=hv ，λh P =如果所考虑的粒子是非相对论性的电子（2c E e µ<<动），那么ep E µ22=如果我们考察的是相对性的光子，那么E=pc注意到本题所考虑的钠的价电子的动能仅为3eV ，远远小于电子的质量与光速平方的乘积，即eV 61051.0×，因此利用非相对论性的电子的能量——动量关系式，这样，便有ph =λnmm mE c hc E h e e 71.01071.031051.021024.1229662=×=××××===−−µµ在这里，利用了meV hc ⋅×=−61024.1以及eVc e 621051.0×=µ最后，对Ec hc e 22µλ=作一点讨论，从上式可以看出，当粒子的质量越大时，这个粒子的波长就越短，因而这个粒子的波动性较弱，而粒子性较强；同样的，当粒子的动能越大时，这个粒子的波长就越短，因而这个粒子的波动性较弱，而粒子性较强，由于宏观世界的物体质量普遍很大，因而波动性极弱，显现出来的都是粒子性，这种波粒二象性，从某种子意义来说，只有在微观世界才能显现。
第13章 量子物理
单色吸收率 (T)：物体吸收的能量与入射能
量之比称为吸收率 .
(T
)
d d
E (吸收) E (入射)
黑体：能完全吸收各种波长电磁波而无反射的 物体，即α=1，黑体是理想化模型。
黑体模型：
不透明介质空腔开一小 孔，电磁波射入小孔后， 很难再从小孔中射出。 小孔表面是黑体。
基尔霍夫辐射定律 在平衡热辐射时
维恩位移定律
辐射最强的波长m与黑体温度T 之间满足
Tm b
b = 2.897×10-3m·K
课本167页例题13-3
13.2光电效应
1.光电效应
当光线照射金属表面时， 金属中有电子逸出的现象， 称为光电效应。逸出的电 子称为光电子。
阳
W
A
极
V
K阴
极
G
2.爱因斯坦的光量子假设
光不仅在发射和吸收时以能量为h的微粒形式出现，
但是，开尔文进一步指出：“在物理晴朗天空的 远处，还有两朵小小令人不安的乌云”，即运用 当时的物理学理论所无法正确解释的两个实验现 象，一个是热辐射现象中的紫外灾难，另一个是 否定绝对时空观的迈克尔逊--莫雷实验。
13.1 黑体辐射
热辐射
物体由大量原子组成，热运动引起原子碰撞使 原子激发而辐射电磁波。原子的动能越大，通 过碰撞引起原子激发的能量就越高，从而辐射 电磁波的波长就越短。
止电压。
由 Ek0 e |UC | h A 可知，
UC
h
e
A e
h e
(
0 )
截止电压与光频率成正比。
13.3 康普顿效应 192223年康普顿研究了X射线在石墨上的散射
X 射线管
晶体
光阑 散射波长,0
量子物理学
Quantum Physics, 2nd量子物理学第二版作者：Gasiorowicz, StephenGasiorowicz, Stephen, Univ. of MinnesotaISBN：0471857378 装帧: cloth出版年代：1995 页码：480出版社：John Wiley & Sons目录原价(USD)：105.95 人民币零售价：250.00读者对象：物理系三年级，四年级到研究生内容简介：Quantum mechanics book with heavy emphasis on applications. Focuses on the physics of the applications, rather than on the mathematical structure. Order of magnitude estimates of effects are presented and calculated in detail. Nonclassical results are reconciled with classical expectations. In addition to core material, this edition contains new material on degenerate matter, the integral Quantum Hall Effect, the Einstein derivation of stimulated emission, lasers and the density matrix, exponential decay, and more. Features 60% more problems.主要章节：The Limits of Classical Physics. Wave Packets and the Uncertainty Relations. The Schrodinger Wave Equation and the Probability Interpretation. Eigenfunctions and Eigenvalues. One-Dimensional Potentials. The General Structure of Wave Mechanics. Operator Methods in Quantum Mechanics. N-Particle Systems. The Schrodinger Equation in Three Dimensions I. The Schrodinger Equation in Three Dimensions II. Angular Momentum. The Hydrogen Atom. Interaction of Electrons with Electromagnetic Field. Operators, Matrices, and Spin. The Addition of Angular Momenta. Time-Independent Perturbation Theory. The Real Hydrogen Atom. The Helium Atom. The Structure of Atoms. Molecules. The Radiation of Atoms. Selected Topics in Radiation Theory. Collision Theory. The Absorption of Radiation in Matter. Appendices. Physical Constants. References. Index.Introduction to Solid State Physics seventh edition固态物理入门第七版作者：Charles KittelISBN：9971511800 （印度版）装帧: Paperback出版年代：1995出版社：John Wiley & Sons人民币零售价：85.00读者对象：本科高年级或者研究生内容简介：New edition of the most widely used textbook on solid state physics in the world. Describes how the excitations and imperfections of actual solids can be understood with simple models that have firmly established scope and power. The foundation of this book is based on experiment, application and theory. Several significant advances in the field have been added including high temperature superconductors, quasicrystals, nanostructures, superlattices, Bloch/Wannier levels, Zener tunneling, light-emitting diodes and new magnetic materials.主要章节：Crystal Structure.Reciprocal Lattice.Crystal Binding and Elastic Constants.Phonons I: Crystal Vibrations.Phonons II: Thermal Properties.Free Electron Fermi Gas.Energy Bands.Semiconductor Crystals.Fermi Surfaces and Metals.Plasmons, Polaritons, and Polarons.Optical Processes and Excitons.Superconductivity.Dielectrics and Ferroelectrics.Diamagnetism and Paramagnetism.Ferromagnetism and Antiferromagnetism.Magnetic Resonance.Noncrystalline Solids.Point Defects.Surface and Interface Physics.Dislocations.AlloysFundamentals of Physics 6th edition基础物理第六版作者：David Halliday, Robert Resnick, Jearl WalkerHalliday在中国高校物理教师中享有广泛声誉，原因除了八十年代中国的翻译介绍之外，更重要的在于该书本身的权威性。
大学物理英文版
Magnitude: r r x 2 y 2 z 2
cos z r
In the two dimension: r r ( t ) x ( t )i y ( t ) j Its two components （分量） x x(t )
三天后 阿姆斯特朗 奥尔德林 柯林斯
Mars(火星）
机遇号
The surface of Mars(火星表面）
Our world and Universe
Universe
Elementary particles
In the view of physics history:
The ancient physics The classical physics The modern physics
Coordinate system （ 坐 标 It is convenient to 系 ）thefixed onsurfaceframe, take : earth’s the relative to frame position, which of as our velocity, in most cases and reference acceleration orbit of course.( What in this the object can be specified quantitatively. cases?) Cartesian Coordinate system(直角坐标系）： o
里德雷时间空间和万物23partonemechanicspartonemechanics24chapterkinematics第一章第一章质点运动学质点运动学kinematicskinematics11参考系质点framereferenceparticle12位置矢量位移positionvectordisplacement13速度加速度velocityacceleration14两类运动学问题twotypesproblems16运动描述的相对性relativemotion15圆周运动及其描述circularmotion理解描述质点运动物理量的定义及其矢量性相对性和瞬时性
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time-dependent 含时间的，时间相关的
free particle 自由粒子
读书如饭，善吃饭者长精神，不善吃者生疾病。——章学诚
plane wave 平面波
wave packet 波包
square well 方势阱
orbital quantum number 轨道量子数
magnetic quantum number
space quantization
Zeeman effect
spin quantum number
most probable electron radius 电子最可几半径
the exclusion principle 不相容原理
scanning electron microscope 扫描电子显微镜
light microscope 光学显微镜
resolution分辨率；决议；解决
atomic spectra 原子光谱
structure of atom 原子结构
absorption spectrum 吸收光谱
Rydberg constant 里德伯常数
energy state 能态（能量本征态）
excited state 激发态
binding energy 束缚能
ionization energy 离子化能量
transition 跃迁
Bohr model 玻尔模型
fine structure 精细结构
disparage 蔑视，毁谤
读书如饭，善吃饭者长精神，不善吃者生疾病。——章学诚
V Quantum Physics (Chapter 33-35)
quantum physics 量子物理学
quantum mechanics 量子力学
classical physics/mechanics 经典物理学/力学
lightbulb 电灯泡
photoelectron 光电子
detector 探测器
burglar 窃ຫໍສະໝຸດ smoke detector 烟雾探测器
photodiode 光控二极管
photosynthesis 光合作用
carbohydrate 糖，碳水化合物
pigment 色素，颜料
chlorophyll 叶绿素
de Broglie wavelength 德布罗意波长
diffraction pattern 衍射图样；衍射花样
aluminum foil 铝箔
electron diffraction 电子衍射
electron microscope 电子显微镜
transmission electron microscope 透射电子显微镜
chemical reaction 化学反应
Compton effect 康普顿效应
incident light 入射光
relativistic particle 相对论粒子
Compton shift 康普顿位移
Compton wavelength 康普顿波长
photon interaction 光子相互作用
spin-orbital interaction 自旋轨道相互作用
fluorescence/phosphorescence 荧光/磷光
laser 激光器
stimulated emission受激发射
Boltzmann distribution 玻尔兹曼分布
population inverse 布居数反转
Planck's quantum hypothesis 普朗克量子假设
special theory of relativity 狭义相对论
blackbody radiation 黑体辐射
spectrum 光谱；频谱；范围
Kelvin temperature 开尔文温度
Wien's law 韦恩定律
philosophic implication 哲学后果
determinism 决定论
Copenhagen interpretation 哥本哈根解释
Schr?dinger's equation 薛定谔方程
time-independent 时间无关的，不含时间的
normalization condition 归一化条件
Balmer series 巴尔摩（谱）系
Lyman series 莱曼系
Paschen series 帕邢系
stationary state 定态
quantum condition 量子化条件
Bohr radius 玻尔半径
ground state 基态
energy level 能级
correspondence principle 对应原理
wave function 波函数
double-slit experiment 双缝试验
probability density/distributioin 概率密度/分布
Heisenberg uncertainty principle 海森伯不确定原理
maximum kinetic energy 最大动能
electrode 电极
stopping potential/voltage 截至电压
light intensity 光强
monochromatic (light) beam 单色光束
collision 碰撞，撞击
work function 功函数
radioactive decay 辐射衰减，放射性衰减
tunnel diode 隧穿二极管
scanning tunneling electron microscope 扫描隧道显微镜
atomic force microscope 原子力显微镜
hydrogen atom 氢原子
principal quantum number 主量子数
the periodic table of elements 元素周期表
electron configuration 电子组态
atomic number 原子序数
total angular momentum 总角动量
Stern-Gerlach experiment 斯特恩-盖拉赫实验
g-factor g-因子
positron 正电子
pair production 电子-正电子的产生
annihilate 湮灭，消灭，消去
wave-particle duality 波粒二象性
the Principle of Complementarity 互补性原理
wave nature of matter 物质的波动本质
boundary condition 边界条件
quantum number 量子数
zero-point energy 零点能
finite potential well 有限深势阱
tunnel 隧穿，隧道
potential barrier 势垒
penetrate 穿透
barrier penetration 势垒穿透
metastable state 亚稳态
holography 全息照相
IV Focal Points (Chatper 33-35)
Failures of classical physics; operator and its eigenvalue problem; Hamiltonian and Hamiltonian operator; Schr?dinger's equation; wave function and its interpretation; normlizaiton of wavefunction; free particle and the particle in an infinite deep square well; energy levels, ground and excited states; nodes; expectation value of observables; potential barrier and tunneling; Quantum theory of hydrogen atom, levels and quantum states of hydrogen atom; photoelectric effect; black-body radiation; Compton effect; wave-particle duality of light; de Broglie wave; uncertainty principle；Bohr's theory of Hydrogen atom.
surface temperature 表面温度
visible spectrum 可见光谱
Rayleigh-Jeans formulations 瑞利-金斯公式
empirical formula 经验公式，经验法则
fit 拟合；与...相符
Planck's constant 普朗克常量
Planck's quantum hypothesis 普朗克量子假设
读书如饭，善吃饭者长精神，不善吃者生疾病。——章学诚
quantized 量子化的
quantum of energy 能量量子